Peak-searching algorithms

The advantage of X-ray powder patterns over other spectra is the roughly common shape of the individual reflections (equal half width and equal shape of the flanks). Therefore, one can use peak search methods that presume a special peak shape. Sanchez (1991) reports a peak search algorithm for Gaussian peaks with an average half width 2D. This method can be easily adapted for Lorentzian peaks (y = A/[l + x — u)/b) ] with FWHM = 2b) or Pearson-VII peaks (y = A/[l + ((x- )/b) f with FWHM = 2b-7( 72-l)). X-ray peaks very often exhibit a peak shape with m between 1.5 and 2. 

Detected by peak search algorithm at routine operational settings. 

The purpose of this study was to evaluate the linear calibration technique employing a single polydisperse standard and the search algorithm described above for non-aqueous and aqueous SEC. Comparison of this calibration technique to peak position, universal calibration, and Q-factor approximation techniques which make use of a series of narrow MWD polystyrene standards was also carried out. 

Spectral searches using a library of reference spectra can be a useful tool in identification. Search algorithms have improved over the years and now use the concept of artificial intelligence. Several software packages can be used to conduct searches in spectral libraries in which the main peaks of known compounds are encoded. The compounds offering the best matches are retained as potential candidates. Library searches involve three stages ... 

The peak search by 2nd derivatives represents a kind of sharpening (deconvolution), i.e. a division by the Fourier transform of a certain peak shape in the frequency domain. This is possible only if this Fourier transform has no zeroes, i.e. if it monotonically approaches zero. Bromba and Ziegler (1984) report such an algorithm, but its usability for X-ray patterns was not proved until now. 

DST methods are particularly competitive for organic compounds, which are more resistant to the traditional approaches and whose structural models can be easily guessed. At present, the complexity of crystal structures solved by direct-space methods is essentially limited by the number of DOFs that can be handled by the global optimization algorithms within a reasonable amount of time. In prospect, improvement of both search algorithms and computer power may overcome this limitation. The major pitfalls for the use of DST are (a) they are time consuming (b) they are dependent on the existence of reliable prior structural information. Partially incorrect models may compromise the success of the procedure independent of the computer time spent (c) they are sensitive to the accuracy of the peak profile parameterization through peak-shape and peak-width functions. ... 

The combined (in quadrature) relative systematic uncertainty bounds for E and V have been determined to be 0.070. This relative systematic uncertainty is within the boundary condition established within the NUREG. It should be stressed that the areas evaluated represent only a portion of the analytical evaluation performed by the current "state-of-the-art software systems. Peak search and complex spectral fitting algorithms have not been addressed directly to date in this evaluation. An attempt will be made to address some of these items in a later section through evaluation of samples containing added isotopes of known quantity. 

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